Topological properties of reflection zeros of optical differentiators based on layered metal-dielectric-metal structures

We investigate the topological properties of reflection zeros of three-layer structures consisting of a dielectric layer sandwiched between two metal layers, which can be used as optical differentiators. We show that the reflection zeros possess non-zero topological charges, which makes them topologically protected. With a small perturbation of the parameters of the structure (e.g., a change in one of the layer thicknesses), the reflection zero does not disappear, but shifts in the parameter space, i.e., appears at different wavelength and angle of incidence. We demonstrate that with a further parameter change, two zeros with opposite topological charges (+1 and -1) approach each other, merge, and then disappear. We believe that the obtained results give useful insight regarding the operation of layered metal-dielectric-metal structures possessing reflection zeros.